Patent Grant
9543925
Field of Invention
The present invention relates generally to apparatus and methods for electrical impedance control and synthesis, and more particularly to impedance control and synthesis by voltage.
Description of the Related Art
Electrical impedance is the measure of the opposition that a circuit presents to the passage of a current when a voltage is applied. In the prior arts, impedance is simulated using active analogue circuits in impedance synthesizers or emulators for a wide range of prescribed resistance, capacitance, and inductance values. As a major application, these impedance values are deployed as reference standards for calibrating electronic test and measurement instruments. During a calibration process, each of the reference components is individually measured by the instrument under calibration and the measured value is compared with the known value from which error of the instrument reading is determined. In general, different instruments may require different reference components. An impedance synthesizer can therefore provide conveniently a myriad of impedance values required for the calibration of many different instruments.
By the way the prior art impedance synthesizer is implemented there are however limitations in the power or voltage handling capabilities for the simulated components. Taking the following patents for example:
U.S. Pat. Nos. 4,963,845, 5,485,115, 5,585,741, 6,351,137, 6,369,650, 6,646,463, 7,808,314 and CN201141879, by which operational amplifiers, digital-to-analog converters, analog-to-digital converters and other linear active circuit elements are deployed in the impedance synthesizer circuits. The relatively low voltage and power handling capabilities of these semiconductor circuit elements have imposed limitations on the power or voltage handling capacities of the impedance synthesized thereof. This is fine for calibrating electronic test and measurement instruments as the impedance values at low signal levels are normally of interest in these applications.
In a different area of application the present invention is exploring however, electrical impedance synthesis techniques can be deployed to control electrical parameters other than instrument calibrations. For example, by varying the impedance of a load synthesized under a supply voltage, a controlled load current is formed. As another example, by controlling the impedance of a load synthesized by an impedance synthesizer and powering the same under at a supply voltage, the amount of power delivered to the load can be controlled. Further, through the control of impedance, and hence the control of current or power, other physical parameters such as temperature, luminosity, pressure, force, speed, etc. can be controlled. The idea, which appears still new to the academic and engineering communities, will be explained in the following specifications of the present invention.
For these applications where high power or high current is required, it would be very difficult and expensive if not impossible to deploy high power operational amplifiers and other active analog devices required for impedance synthesis in the traditional way, even if power efficiency is not taken into consideration.
Accordingly, the present invention intends to explore a new area of electronic power control through the creation of a novel voltage controlled impedance synthesizer with the following features:
According to an embodiment of the present invention, a voltage controlled impedance synthesizer provides stepwise variable impedance values according to a prescribed function of the control voltage, said synthesizer comprises of one or more two-terminal impedance modules connected in series, in each impedance module one or more essentially identical two-terminal impedance elements connected in series, a corresponding number of switches to short out by selection none to all of the impedance elements in the impedance module, and said switches being controlled by the control voltage through analog-to-digital conversion and digital processing means. The values of the impedance elements between the impedance modules in ratios being uniquely defined according to the numbers of impedance elements in the impedance modules, the voltage controlled impedance synthesizer is controlled to provide monotonic and stepwise variable impedance values. Further, through the use of the voltage controlled impedance synthesizer, other electrical parameters such as current and power can be controlled according to any prescribed functions.
Furthermore, by the duality property of electrical circuits, the present invention can be applied also to the synthesis of electrical admittance, as will be elaborated in the following description.
The operation principle of the Voltage Controlled Impedance Synthesizer VCZS as an embodiment of the present invention is illustrated by the block diagram of
The area of application of a Voltage Controlled Impedance Synthesizer VCZS as deployed in an exemplary feedback control system and as illustrated by the block diagram of
It is therefore desirable for the above application to provide an apparatus or a method for synthesizing impedance values through circuit switching of a combination of component impedance elements, to vary in a series of steps accurately and speedily within a predetermined control range. It is also desirable that any variation of the impedance synthesized is monotonic, i.e. the controlled impedance always increases or remains constant as the value representing the controlling digital input increases, while the controlled impedance always decreases or remains constant as the value representing the controlling digital input decreases. Monotonicity is required as an essential characteristic for stability for a control system. Further it is also desirable to have any variation of the impedance synthesized in steps of equal magnitudes, a feature essential to the fineness of control.
The digital approach as adopted by various embodiments of the present invention is through switching in and out of “Impedance Elements” by a Digital Impedance Synthesizer, DZS as illustrated by
Over the past decades, many different switching circuit topologies have been invented for other areas of application, such as that for AC voltage regulation. In general, when the number of steps is increased for the purpose of achieving finer control, the number of states of the switches and hence the actual number of switches required will inevitably increase. Since the switches are the key and relatively expensive components of the system, precision of control has often been compromised for lowering down the system cost by limiting the number of switches employed. This is highly undesirable and many different varieties of switching circuit topologies and control methods have been attempted in the past to achieve higher control accuracy while limiting the number of switches employed for circuit simplicity and cost reduction. However these existing designs are in general complicated in overall system structure, and are therefore difficult to be designed and deployed.
Further, as fine steps are achieved with sufficiently large number of switching states, higher control accuracy becomes feasible, bring in a new challenge to the designers. Dependent of the actual circuit design and the precision in circuit implementation, linearity or even monotonicity relationship between the digital control signal and the controlled impedance might be lost as the size of the steps decreases, leading possibly to system instability and/or reduction in control accuracy and thus imposing a very challenging task to the designer.
In fact, there is an issue on the practical limitations affecting the linearity and monotonicity of the Voltage Controlled Impedance Synthesizer VCZS, i.e. the accuracy of the Impedance Elements ZEs. It can be shown that when the Impedance Elements ZEs are not made sufficiently accurate and matched with each other well in right ratios, the linearity and monotonicity could not be achieved. Consequently the performance of the Voltage Controlled Impedance Synthesizer VCZS, in terms of control accuracy and system stability, is likely compromised if this aspect in system design is not properly addressed.
Apart from practical limitations of components available, there is no restriction by the present disclosed approach in designing the Voltage Controlled Impedance Synthesizer VCZS in terms of control accuracy, number of switches deployed, the total number and values of impedance elements. The method of control and the associated control circuitry is simple and straight forward, while the practical limitations affecting the linearity and monotonicity will be addressed to have its consequent bad effects removed too.
Additional applications and advantages of the invention will become apparent from the following description and the accompanying drawings. It is understood that changes in the specific structure shown and described may be made without departing from the scope and spirit of the invention.
With the foregoing in view, as other advantages as will become apparent to those skilled in the art to which this invention relates as this patent specification proceeds, the invention is herein described by reference to the accompanying drawings forming a part hereof, which includes descriptions of some typical preferred embodiments of the principles of the present invention, in which:
Glossary:
The invention will now be described more specifically with reference to the figures. It is to be noted that the following descriptions of preferred embodiments of this invention are prepared herein for purpose of illustration and description only. It is not intended to be exhaustive or to be limited to the exact forms disclosed, since the Voltage Controlled Impedance Synthesizer according to the invention may be advantageously used and modified in various fields.
Here “digital processing means” refers to any digital devices or apparatus deployed for the necessary digital logic operations.
The Digital Impedance Synthesizer DZS comprises of one or more two-terminal impedance modules connected in series, each impedance module having one or more essentially identical two-terminal impedance elements connected in series, and a corresponding number of switches to short out by selection none to all of the impedance elements in the impedance module. By making the values the impedance elements between the impedance modules in ratios uniquely defined according to the numbers of impedance elements in the impedance modules, and by controlling the said switches through the Switch Pattern Encoder SPE implemented by digital processing means, the digital impedance synthesizer can be controlled to provide monotonic and stepwise variable impedance values according to the controlling voltage Vcon(t). More details of the explanation of the operation principle of the Digital Impedance Synthesizer DZS is following.
Within each of the Impedance Modules ZMs, there are one or more two-terminal Impedance Elements ZEs connected in series, the Impedance Elements ZEs being in galvanic isolation before said connection, the total number of ZEs in the mth Impedance Module ZMs being Nm, where m=1 to MZM.
Within each of the Impedance Modules ZMs, all the Impedance Elements ZEs have essentially the same impedance values, even for the impedance elements with non-linear characteristics, such as diodes. In other words, the nominal impedance values of the Impedance Elements ZEs is
Zm1=Zm2=Zm3= . . . =Zmc where c=1 to Nm, i.e.
for any of the Impedance Module ZMm. For non-linear impedance elements, the equality still holds as by design the same current level is always passing through every one of all the elements in each Impedance Module ZM. The same value of impedance is designated Zm as the nominal impedance in the mth Impedance Module ZM.
Within each of the Impedance Modules ZMs, all the Impedance Elements ZEs are connected in series such that each Impedance Element ZE is adding directly to the overall impedance of the Impedance Module ZM. In other words, the largest impedance achievable from the Impedance Module ZM is the direct arithmetic sum of impedances from all the Impedance Elements ZEs within the Impedance Module ZM, i.e. Zm×Nm in the mth Impedance Module ZM.
Further, an additional requirement is that the impedance elements in all the impedance modules are of essentially the same quality factor at the frequency of application. In other words, the ratio of reactance to resistance of any impedance element is the same as any other impedance elements. By this, the combined impedance of any number of impedance elements for all impedance modules connected in series can be determined by direct summation of the respective resistance and reactance values respectively.
Within each Impedance Module ZM, such as ZM2 as an example for illustration, for which the number of Impedance Elements ZEs is N2=4. As shown, the switches designated by S21, S22, S23 and S24 are connected in parallel with the series of Impedance Elements ZEs such that one terminal of each of all the switches are connected together to one of the two output terminals To21 and To22 of the Impedance Module ZM2, say To21 as shown in
Alternatively, the switches S21, S22, S23 and S24 can be connected to perform the same function with one terminal of each of all the switches connected together to the output terminal To22 instead (and not to To21!), the other terminals of all switches are connected with S21 to To21 which is connected to the fourth Impedance Element ZE24, S22 to the terminal connecting Impedance Elements ZE3 and ZE4, S23 to the teiminal connecting Impedance Elements ZE22 and ZE23, and S24 to the terminal connecting Impedance Elements ZE21 and ZE22, i.e. S2i to the terminal connecting the Impedance Elements ZE2(N2−i+1) and ZE2(N2−i+2).
Note that a switch is an electrical component that can make and break an electrical circuit, interrupting the current or diverting it from one conductor to another. The switches mentioned herein are therefore not limited to any form or any kind, such as those of mechanical contact switches, relay switches, contactors, semiconductors switches such as MOSFETs, JFETs, IGBTs, BJTs, Thyristors, solid-state-relays, etc.
The property of monotonicity refers to a way how the synthesized impedance of a Digital Impedance Synthesizer DZS follows the controlling digital input, i.e. the controlled impedance always increases or remains constant as the value representing the controlling digital input increases, while the controlled impedance always decreases or remains constant as the value representing the controlling digital input decreases. According to various embodiments of the present invention, for all Impedance Elements ZEs in all Impedance Modules ZMs, i.e. ZEmc for cth ZE in mth ZM, for c=1 to Nm, m=1 to MZM, proper weightings are assigned to the various nominal impedance Zm among the Impedance Modules ZMs. A necessary condition for achieving monotonicity has to be met as follows:
Assigning the lowest weighting to ZM1, then progressively higher weightings for ZM2, ZM3, ZM4, etc., then the conditions for monotonicity are:
Further, for linearity relationship between the synthesized impedance of a Digital Impedance Synthesizer DZS and the controlling digital input, i.e. there is yet another condition required to be met according to some embodiments of the present invention:
The ratios of the magnitudes of impedance Zm of the Impedance Elements ZEs between the Impedance Modules are uniquely defined according to the numbers of Impedance Elements ZEs in the Impedance Modules ZMs with lower weightings compared to that of the Impedance Module under consideration, as defined by the following equation:
Z1:Zm=1: Π(Ni1+1) where i=1 to m−1, m=1 to MZM.
For example, Z1:Z2=1:(N1+1),
As an example for illustration, let a Digital Impedance Synthesizer DZS be constructed with three Impedance Modules, ZM1, ZM2 and ZM3:
For ZM1: N1=4
For ZM2: N2=3
For ZM3: N3=5
Let Z1=10 ohm, then Z1:Z2=10:Z2=1: (N1+1)=1:5, therefore Z2=50
Z1:Z3=1:(Ni+1)×(N2+1), then 10:Z3=1:5×4=1:20, therefore Z3=200
Thus the Digital Impedance Synthesizer DZS so constructed will have a total of three Impedance Modules each with 4, 3 and 5 Impedance Elements with values each 10, 50 and 200 ohms respectively. Total number of switch states is (4+1)×(3+1)×(5+1)=120, synthesizing 120 impedance values from 0 to (10×4)+(50×3)+(200×5)=1190 ohms in steps of 10 ohms.
It can be verified easily by the above example that when the necessary conditions for linearity are met, conditions for monotonicity are also satisfied.
Assume that the above conditions for linearity are met for what are shown in
Hence by turning on the appropriate one of the four switches in the Impedance Module ZM2, i.e. S2i in ZM2, for i=1 to 4, the output of the Impedance Module ZM2, i.e. Z2o, can be varied monotonically from 0 to 4×Z2 in equal steps of Z2. In general for any Impedance Module ZM, by turning on the appropriate ones of the switches in the Impedance Module ZM, i.e. Smi in ZMm, for i=1 to Nm, the output of the Impedance Module ZMm, i.e. Zmo, can be varied monotonically from 0 to ZmNm in equal steps of Zm. Note that when S2i is shorted, the status of S2(i+j) is immaterial for j=1 to Nm−i.
It is also obvious that for all the Impedance Modules ZMs, by turning on the appropriate switches in each of the Impedance Modules ZMs, the overall impedance of the Digital Impedance Synthesizer ZDZS can be varied monotonically from 0 to ΣZm×Nm for m=1 to MZM, in equal steps of Z1, and in a total of Π(Nm+1) steps, for m=1 to MZM.
In general when the impedance of Impedance Element ZE is of a complex value, i.e. Zm=Am+jBm, A being the resistive component and B being the reactive component, for m=1 to MZM, the largest impedance value achievable from the Impedance Module ZMm is the direct arithmetic sum of impedances from all the Impedance Elements ZEs within the Impedance Module ZMm, i.e. Zm×Nm=Am×Nm+jBm×Nm. For all the Impedance Modules ZMs, by turning on the appropriate switches in each of the Impedance Modules ZMs, the overall impedance synthesized by the Voltage Controlled Impedance Synthesizer ZVCZS can be varied monotonically from 0+j0 to ΣZm×Nm, i.e. from 0+j0 to Σ(Am+jBm)×N for m=1 to MZM, in equal steps of Z1, and in a total of Π(Nm+1) steps, for m=1 to MZM.
In practice, due to various reasons, such as the tolerance in the electrical parameters of the Impedance Elements ZEs, the non-linearity of the Impedance Element ZEs, and the contact impedance of the switches that might be considered attributed to the Impedance Elements connected to, etc., there is likely some deviation in the actual impedance value of Zmc from the nominal impedance value of the Impedance Elements.
Designating this deviation by δZmc, and assuming δZa is the largest deviation for any of ALL Impedance Elements ZEs in ALL Impedance Modules ZMs, i.e. the largest among all δZmc, c=1 to Nm, m=1 to MZM, the maximum deviation of Zmo, the maximum impedance of the mth Impedance Module ZM from its nominal value is δZmo, then δZmo=δZa×Nm.
Therefore, in comparison to the nominal impedance values, the deviation of ZVCZS, the output of the Voltage Controlled Impedance Synthesizer VCZS, is δZVCZS, and the maximum value of δZVCZS=ΣδZmo is:
δZVCZS=ΣδZmo=ΣδZa×Nm=δZa×ΣNm where m=1 to MZM.
If the steps are controlled such that each time one and only one Impedance Element ZE in any of the Impedance Modules ZMs is added to or removed from contributing to the output of the Impedance Module ZM, the maximum change in the impedance deviation from the nominal, at each step change of the Impedance Module, would be δZa, and total change in the impedance deviation from the nominal impedance ZVCZS for the Voltage Controlled Impedance Synthesizer VCZS, is δZVCZS=|δZa|×MZM
In order to make sure that the impedance change under control is monotonic, it is required that
|δZVCZS|<Z1i.e. |δZa|×MZM<Z1,i.e. |δZa|<Z1/MZM
In other words, the deviation of impedance of any of the Impedance Elements ZEs would need to be less than the nominal impedance value of the smallest (least significant) Impedance Element ZE divided by the total number of Impedance Modules ZMs, MZM.
Hence to achieve linearity relationship between the synthesized impedance of a Digital Impedance Synthesizer DZS and the controlling digital input in practice the values of the Impedance Elements in each of all the Impedance Modules need to be substantially close to the theoretical values required as necessary conditions for linearity, such that the ratios of the impedance values of each one Impedance Element ZE between the Impedance Modules ZMs would need to be bounded by the following equation:
Z1:Zm=1: [Π(Ni+1)]±|δZa|/Z1=1: [Π(Ni+1)]±1/MZM where i=1 to m−1, for m=1 to MZM.
Shown in
Referring back to
f(t)=VI=K1·Iload where K1 is a constant, then
Iload=f(t)/K1,
i.e., the load current Iload tracks proportionally to the function f(t), irrespective of any variations of the supply voltage of and change of the load impedance.
A typical and useful case is that f(t) is a constant voltage,
f(t)=K2=K1·Iload, therefore
Iload=f(t)/K1=K2/K1, which is also a constant,
i.e. the load current is controlled constant despite of any variations of the supply voltage of and change of the load impedance.
If, instead of f(t), VI is compared to the voltage VS of the supply voltage Vsup, VS being sensed and scaled appropriately by the voltage sensor Vsense, as shown in
f(t)=VS=K2·Vsup=VI=K1·Iload, leading to
Vsup/Iload=K1/K2=ZVCZS
i.e., the impedance as the output of the Voltage Controlled Impedance Synthesizer VCZS is controlled to remain constant, and also linear, even if the individual composing elements, such as the LEDs for example, of the impedance synthesizer are not linear.
Further, as yet another exemplary embodiment of the invention, power can also be controlled constant by the Voltage Controlled Impedance Synthesizer VCZS, as illustrated in
f(t)=Vs=K2·Vsup
VI=K1·Iload
Hence, PWR=Vs·VI=K2·Vsup·K1·Iload
When Vcon(t) is sufficiently small by the action of negative feedback control, i.e.
Vcon(t)=PWRset−PWR=0
PWRset=PWR=K2·Vsup·K1·Iload
Therefore the power supplied to the load ZVCZS is
Vsup·Iload=PWRset/(K1·K2)
which is a constant as long as PWRset remains constant.
Hence, the power of the load ZVCZS is maintained constant despite of any variations of the supply voltage Vsup or the load impedance ZVCZS.
As another practical example of application of the Voltage Controlled Impedance Synthesizer VCZS as an exemplary embodiment of the invention, a light-emitting device directly powered from an AC power supply is illustrated in
As shown, the LED diodes are connected in series as basic Impedance Elements ZEs. There are two Impedance Modules ZMs, ZM1 and ZM2. ZM1 is comprising four LEDs D11, D12, D13 and D14. ZM2 is comprising five LED strings D21, D22, D23, D24 and D25, each string comprising five LEDs. D00, a string of one or more LEDs, is connected in series with the Voltage Controlled Impedance Synthesizer VCZS so as to provide a non-zero impedance value of the light-emitting device at the “zero impedance” state of the Voltage Controlled Impedance Synthesizer VCZS, and to add to the total impedance value of the light-emitting device at any digital state of the synthesizer. The series of LEDs D00, in series with the LEDs in the Voltage Controlled Impedance Synthesizer VCZS, provide the lighting output from the light-emitting device. By design D00 can balance out excessive DC voltage as rectified from the supply Vac by the bridge rectifier formed of the rectifier diodes D1, D2, D3 and D4, which effectively extends the supply input voltage range of Vac so that the current through the light-emitting device is limited to a prescribed safe value within the control range of the Voltage Controlled Impedance Synthesizer VCZS. However, due to the non-linearity characteristics of the LED diodes, D00 will also extend the non-conducting portion of the mains cycle, hence reducing the effectiveness of the LED device as a whole. As a modified version of the embodiment, the series of LEDs D00 can be replaced by a current limiting device for over current protection, but without contributing to the luminous output of the light emitting device.
Assuming all the LEDs bear the same impedance value at any particular current, the ratio of the values of impedance elements between ZM1 and ZM2 is 1 to 5. Therefore there are as shown five LED diodes in each segment of the Impedance Module ZM2 while only one in ZM1. The Impedance Module ZM1 comprises four switches S11, S12, S13 and S14 which are controlled by a Modulo-5 (Quinary) up-down counter Cs1 in the ADC. Likewise, the Impedance Module ZM2 comprises five switches S21, S22, S23, S24 and S25 which are controlled by a Modulo-6 (Senary) up-down counter CS2 in the ADC.
Not explicitly shown in the diagram, the output of the counter Cs1 is already encoded to provide one single digit active for one counting state, so that S11 only is turned on at count state 0, S12 only is on at counter state 1, S13 only is on at counter state2, S14 only is on at counter 3, and no switch is on at counter state 4. This can be easily achieved by a binary-to-decimal encoder for example, working with a binary counter.
As shown, when S11 is closed, all the LEDs in ZM1 are short-circuited. When S12 is closed, all except D11 are short-circuited. When S13 is closed, only D11 and D12 are not short-circuited. When S14 is closed, only D14 is short-circuited. When all circuits are open, all four LEDs are not short-circuited. Hence the impedance of the Impedance Module ZM1 can be controlled by the four switches to step through five different values, i.e. 0, Z1, 2Z1, 3Z1 and 4Z1 where Z1 is the impedance value of a single LED. Similarly the impedance of the Impedance Module ZM2 can be controlled by the five corresponding switches driven by the counter CS2 to step through six different values, i.e. 0, 5Z1, 10Z1, 15Z1, 20Z1 and 25Z1.
The various states of the switches and the corresponding impedance values synthesized in multiples of a single LED are listed out in the following table:
Therefore, as shown by the table, by controlling the switch states of the two Impedance Modules ZM1 and ZM2 for a total of 30 states, the impedance of the Voltage Controlled Impedance Synthesizer VCZS, i.e. ZVCZS, is stepped from 0 to 29 in steps of one, each step being equivalent to the impedance of one single LED.
As shown in
Note the analog-to-digital converter ADC deployed for the present embodiment is an ordinary tracking ADC with two up/down counters Cs1 and Cs2, of Modulo-5 and Modulo-6 respectively. In general, any ADC will do the job provided the digital output, encoded as necessary, matches the design of the Digital Impedance Synthesizer DZS as described.
Apart from the availability of many different sorts of ADCs that can be chosen for deployment, note also that there is much more room for design variation of the Voltage Controlled Impedance Synthesizer VCZS as different embodiments of the invention. By selecting the number of Impedance Modules ZMs and the number of Impedance Elements ZEs in each Impedance Module ZM, there is infinite number of variations of the Voltage Controlled Impedance Synthesizer VCZS. A best embodiment of the invention can therefore be chosen to suit individual design targets, such as those for optimizing control accuracy, control range, number of switches, switch driving and controlling circuit topology, parts availability, system stability, total implementation cost, etc. The vast number of variations available by the invention provides much design flexibility in choosing the best approach for any application intended.
Further, by duality property of electrical circuits, all circuit principles described for impedance synthesis in this application can also be applied to admittance synthesis. As an exemplary embodiment of present invention the basic architecture of a Digital Admittance Synthesizer DAS is shown in
Although the invention and its advantages have been described in detail, it should be understood that various changes, substitutions, and alterations can be made therein without departing from the spirit and scope of the invention as described. That is, the discussion included in this application is intended to serve as a basic description. It should be understood that the specific discussion may not explicitly describe all embodiments possible; as many alternatives are implicit. It also may not fully explain the generic nature of the invention and may not explicitly show how each feature or element can actually be representative of a broader function or of a great variety of alternative or equivalent elements. Again, these are implicitly included in this disclosure. Where the invention is described in device-oriented terminology, each element of the device implicitly performs a function. Neither the description nor the terminology is intended to limit the scope of the invention.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/IB2013/058250 | 9/3/2013 | WO | 00 |
| Publishing Document | Publishing Date | Country | Kind |
|---|---|---|---|
| WO2014/033694 | 3/6/2014 | WO | A |
| Number | Name | Date | Kind |
|---|---|---|---|
| 7830095 | Erhardt | Nov 2010 | B2 |
| 9100046 | Granger-Jones | Aug 2015 | B2 |
| Number | Date | Country | |
|---|---|---|---|
| 20150229294 A1 | Aug 2015 | US |
| Number | Date | Country | |
|---|---|---|---|
| 61696238 | Sep 2012 | US | |
| 61734948 | Dec 2012 | US |
